Interferometry is central to research and industrial applications such as high-precision metrology (Cho S.-B., and Noh T.-G. “Stabilization of a long-armed fiber-optic single-photon interferometer.” Optics express 17, no. 21 (2009): 19027-19032, incorporated herein by reference in its entirety, hereinafter Cho), optical coherence tomography (Huang D., Swanson E. A., Lin C. P., Schuman J. S., Stinson W. G., Chang W., Hee M. R., Flotte T., Gregory K., and Puliafito C. A. “Optical coherence tomography.” Science 254, no. 5035 (1991): 1178-1181, incorporated herein by reference in its entirety, hereinafter Huang), and quantum optics experiments (Marcikic, Toliver P., Dailey J. M., Agarwal A., and Peters N. A. “Continuously active interferometer stabilization and control for time-bin entanglement distribution.” Optics Express 23, no. 4 (2015): 4135-4143, incorporated herein by reference in its entirety, hereinafter Toliver), and is critical for certain quantum communications/key distribution protocols (Goldenberg L., and Vaidman L. “Quantum cryptography based on orthogonal states.” Physical Review Letters 75, no. 7 (1995): 1239, incorporated herein by reference in its entirety, hereinafter Goldenberg; Koashi M., and Imoto N. “Quantum cryptography based on split transmission of one-bit information in two steps.” Physical review letters 79, no. 12 (1997): 2383, incorporated herein by reference in its entirety, hereinafter Koashi; Noh T.-G. “Counterfactual quantum cryptography.” Physical review letters 103, no. 23 (2009): 230501, incorporated herein by reference in its entirety, hereinafter Noh). Fiber-based interferometry specifically is a robust and scalable platform for these applications, due to the availability, low cost, and ease of use of components. However, various environmental factors such as thermal, acoustic, and mechanical perturbations change the optical path difference between interferometer arms and cause drifts and random fluctuations in interferometer phase. The large uncertainty in the phase reduces control over how precisely a signal can be interfered by the interferometer, introducing measurement uncertainties. In order to guarantee precise measurements and long-term phase stability, phase stabilization techniques are employed.
Optical interferometer stabilization methods include passive methods, which usually attempt to minimize the impact or amount of environmental fluctuation (e.g. through temperature control or isolation from vibration), and active stabilization methods, which use real-time control to rectify instabilities. However, as the impact of environmental factors is only reduced (and not eliminated) with passive stabilization methods, these are insufficient on their own for long-term operational stability and they must usually be combined with active stabilization techniques.
Recently, interest in active stabilization methods for the fiber-optic interferometer platform has been driven by applications such as quantum communications and experimental realizations of quantum key distribution protocols, quantum optics experiments (Cho), and the generation of special non-classical states of light (such as time-bin entangled qubits) for quantum information processing applications (Toliver).
Optical coherence tomography (OCT) and other interferometric sensing approaches are non-invasive measurement techniques that can be used to extract depth or material information using the known optical phase of an interferometer. Increasing their measurement resolution, or equivalently, the precision of the optical phase readout, is therefore highly relevant for these applications.
Interferometer phase-readout and active stabilization methods to date have largely been limited to the use of a small phase modulation (dither) in an interferometer arm (Freschi A. A., and Frejlich J. “Adjustable phase control in stabilized interferometry.” Optics Letters 20, no. 6 (1995): 635-637, incorporated herein by reference in its entirety, hereinafter Freschi), the injection of an additional laser reference signal into the interferometer (Cho and Marcikic I., de Riedmatten H., Tittel W., Zbinden H., Legré M., and Gisin N., “Distribution of time-bin entangled qubits over 50 km of optical fiber.” Phys. Rev. Lett. 93(18), 180502 (2004), incorporated herein by reference in its entirety, hereinafter Marcikic), and variants of the Pound-Drever-Hall laser frequency stabilization scheme (Rogers S., Mulkey D., Lu X., Jiang W. C., Lin Q., “High visibility time-energy entangled photons from a silicon nanophotonic chip.” (2016): arXiv:1605.06540, incorporated herein by reference in its entirety, hereinafter Rogers).
Existing stabilization methods (e.g. reference lasers) and many interferometric sensing approaches that make use of feedback/phase-readout signals periodic in phase (like interference fringes) cope with intrinsic phase-readout ambiguities. Specifically, a single readout-signal level usually corresponds to more than one unique phase; the readout-signal is not a one-to-one function of the phase. Additionally, the phase at readout-signal maxima/minima is difficult to precisely define as these points have a low phase derivative; a large change in phase corresponds to only a small change in the readout signal. Phase readout and stabilization schemes that address these issues do so at the expense of reduced precision in phase control or a greatly increased setup complexity/cost. For example, dithering adds an additional noise source that degrades output quality in applications such as quantum optics (Grassani D., Galli M., and Bajoni D. “Active stabilization of a Michelson interferometer at an arbitrary phase with subnanometer resolution.” Opt. Lett. 39(8), 2530-2533 (2014), incorporated herein by reference in its entirety, hereinafter Grassani), while variants of the Pound-Drever-Hall method greatly increase setup complexity (Rogers).
Many stabilization methods for free-space interferometer setups allow precise phase-readout and arbitrary-phase stabilization (Grassani), but are either too complex, costly, or simply not transferable to fiber-optic interferometers (which have issues unique to the fiber platform, such as birefringence shifts in the interferometer arms).
Therefore, despite the development of phase-readout methods in optical interferometers as well as active stabilization schemes, these methods and systems are usually limited to one particular implementation and especially for fiber interferometers, several phase-readout issues still need to be addressed. For interferometric sensing and interferometer stabilization applications, the following issues are not yet solved in all platforms: (i) intrinsic phase ambiguities due to the periodicity of feedback signals (Grassani); (ii) phase ambiguity at feedback signal extrema (it is difficult to accurately stabilize on maxima/minima due to the low signal derivative and potential sign-change of the feedback signal). As the precision of phase-readout determines the precision of measurement, phase-stabilization and control, there exists a need for state-of-the-art systems and methods for phase readout/control and active stabilization particularly compatible with fiber-based interferometers.